Chapter 7 - Section 7.2 - Trigonometric Integrals - 7.2 Exercises - Page 499: 23

$\tan x - x + C$

$$\eqalign{ &\text{Let } I= \int {{{\tan }^2}x} dx \cr & {\text{Rewrite the integrand using }}{\tan ^2}\theta = {\sec ^2}\theta - 1 \cr & I = \int {\left( {{{\sec }^2}x - 1} \right)} dx \cr & = \int {{{\sec }^2}x} dx - \int {dx} \cr & {\text{Using basic formulas of integration we obtain}} \cr & I = \tan x - x + C \cr} $$